Geodesic
Finite surgeries on three-tangle pretzel knots
Futer, David1 ; Ishikawa, Masaharu2 ; Kabaya, Yuichi3 ; Mattman, Thomas W4 ; Shimokawa, Koya5
1 Mathematics Department, Temple University, Philadelphia, PA 19122, USA
2 Mathematical Institute, Tohoku University, Sendai, 980-8578, Japan
3 Department of Mathematics, Tokyo Institute of Technology, 2-12-1 Oh-okayama, Meguro-ku, Tokyo 152-8551, Japan
4 Department of Mathematics and Statistics, California State University at Chico, Chico, CA 95929-0525, USA
5 Department of Mathematics, Saitama University, Saitama 338-8570, Japan
Algebraic and Geometric Topology, Tome 9 (2009) no. 2, pp. 743-771

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

We classify Dehn surgeries on (p,q,r) pretzel knots that result in a manifold of finite fundamental group. The only hyperbolic pretzel knots that admit nontrivial finite surgeries are (−2,3,7) and (−2,3,9). Agol and Lackenby’s 6–theorem reduces the argument to knots with small indices p,q,r. We treat these using the Culler–Shalen norm of the SL(2, ℂ)–character variety. In particular, we introduce new techniques for demonstrating that boundary slopes are detected by the character variety.

DOI : 10.2140/agt.2009.9.743
Keywords: pretzel knot, exceptional Dehn surgery, finite surgery, Culler–Shalen seminorm

Futer, David 1 ; Ishikawa, Masaharu 2 ; Kabaya, Yuichi 3 ; Mattman, Thomas W 4 ; Shimokawa, Koya 5

1 Mathematics Department, Temple University, Philadelphia, PA 19122, USA
2 Mathematical Institute, Tohoku University, Sendai, 980-8578, Japan
3 Department of Mathematics, Tokyo Institute of Technology, 2-12-1 Oh-okayama, Meguro-ku, Tokyo 152-8551, Japan
4 Department of Mathematics and Statistics, California State University at Chico, Chico, CA 95929-0525, USA
5 Department of Mathematics, Saitama University, Saitama 338-8570, Japan 
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     title = {Finite surgeries on three-tangle pretzel knots},
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Futer, David; Ishikawa, Masaharu; Kabaya, Yuichi; Mattman, Thomas W; Shimokawa, Koya. Finite surgeries on three-tangle pretzel knots. Algebraic and Geometric Topology, Tome 9 (2009) no. 2, pp. 743-771. doi: 10.2140/agt.2009.9.743

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